2. The sales manager of a publisher of university textbooks has six traveling sa

Question

2. The sales manager of a publisher of university textbooks has six traveling sales staff to assign to three different regions. She has decided that each region should be assigned one or more dedicated sales staff. The estimated sales per region varies with the number of staff assigned as follows Region 2 21 42 56 70 Region 3 No. of sales staff 2 4 Region 1 35 48 60 69 41 53 65 Use dynamic programming to determine how the six travelling sales staff should be assigned to the three regions to maximize the total sales.

Explanation / Answer

Let Sn = Sales people remaining

Xn = workers to assign to region n

Mn(Xn) = Expected increase in sales if Xn sales people are assigned to region n

F*n Sn = Mn (Xn) + F*n+1 (Sn - Xn)

For N = 3

For N = 2

For N = 1

S3 F*3 (S3) X3* 1 28 1 2 42 2 3 63 3 4 75 4

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